1. Field of the Invention
The invention is drawn to a method and apparatus for sensing the soil water content and soil bulk electrical conductivity (BEC). Moreover, the water content and BEC may be determined to arbitrary depths in discrete intervals for managing the irrigation of plants, studying and managing environmental interventions and any other applications.
2. Description of the Prior Art
Soil water content and bulk electrical conductivity have both been sensed by electronic systems that measure the electrical response to an imposed electromagnetic (EM) signal. Such systems differ in the nature of the imposed EM signal, the nature of the measured electrical response, and the nature of the electronic circuitry used and its ability to measure various aspects of the electrical response. Three main measurement paradigms exist; those based on capacitance, those based on time domain transmission measurements; and those based on time domain reflectometry.
Systems known as capacitance systems impose an oscillating sinusoidal electrical wave to one or more pairs of electrodes, using one of many possible oscillator circuits, and measure the resonant frequency at which the electronic oscillator system stabilizes. Each pair of electrodes constitutes a capacitor which is part of the oscillator circuit. The electrodes may or may not be in contact with the soil, but if not in contact, then the electrodes are close enough to the soil that the fringing EM field of the capacitor (electrode pair) invades the soil to some extent. Either arrangement makes the soil medium part of the dielectric material involved in the capacitor formed by the electrodes. The capacitance of said capacitor is a function of the electrode geometry and the dielectric permittivity of the medium invaded by the EM field the capacitor. As the soil water content increases the dielectric permittivity of said medium increases and the frequency of oscillation decreases. Calibration against water content may be in terms of frequency, scaled frequency, or some quantity derived through a theoretical transformation such as the permittivity. Although earlier examples exist, the design of Dean et al. (1987, Soil moisture measurement by an improved capacitance technique: Part I. Sensor design and performance. J. Hydrol. 93:67-78) was the prototype for many existing capacitance systems that are deployed as electrode pairs inside a plastic access tube installed in the soil such that the fringing field invades the soil surrounding the access tube.
The down-hole capacitance sensors all employ a capacitive sensor consisting of two cylindrical electrodes arranged along a common axis and separated by a space that is typically filled with a plastic. This arrangement is placed in an access tube composed of some sort of plastic or plastic-fiberglass composite, which itself is inserted into the soil. The electrodes are connected to an oscillating circuit that settles to a resonant frequency that will change it the dielectric properties of the soil material around the access tube change. Since the two electrodes are in the access tube, most of the EM field developed between the electrodes is itself confined to within the access tube. Only a small part of the EM energy, called the fringing field, enters and interacts with the soil. The volume of soil penetrated by the EM field is static, although we now know that its exact shape and volume are dependent on the arrangement of the resistive and capacitive elements of the soil outside the access tube. The capacitance of the soil-access tube system, C (F), is given by (Dean et al., 1987, ibid):C=g∈a∈o  [1]where ∈a is the system apparent relative permittivity (−), ∈o is the permittivity of free space (F/m) and the geometric constant, g (m), has a value dependant on the geometry of the system. The resonant frequency, F (Hz), is given by (Dean et al., 1987):F=[2π(L)0.5]−1(C−1+Cb−1+Cc−1)0.5  [2]where Cb and Cc are the electrode capacitances including the capacitances of internal circuit elements to which the electrodes are connected, C is the capacitance of the soil-access tube system defined in Eq. [1], and L is the inductance (henries) of the coil in the LC oscillating circuit. As soil water content increases, C increases in concert with the increasing soil apparent permittivity, and F decreases.
Multiple field and laboratory studies have shown that capacitance sensors used in access tubes were much less well correlated with field measured water contents than was the neutron probe (Evett and Steiner, 1995, Precision of neutron scattering and capacitance type soil water content gauges from field calibration. Soil Sci. Soc. Amer. J., vol. 59, pp. 961-968; Evett et al., 2006, Soil profile water content determination: Sensor accuracy, axial response, calibration, temperature dependence and precision. Vadose Zone J. 5:894-907; Evett et al., 2009, Soil profile water content determination: Spatiotemporal variability of electromagnetic and neutron probe sensors in access tubes. Vadose Zone J. 8(4):926-941; and Mazahrih et al., 2008, Field Calibration Accuracy and Utility of Four Down-Hole Water Content Sensors, Vadose Zone Journal, vol. 7, no. 3, p. 992). Also, standard deviations of profile soil water content determined by capacitance sensors and by a down-hole quasi-TDR sensor were larger than those determined using the neutron probe or gravimetric sampling by hydraulic push probe, so much so that numbers of access tubes and sensors required to obtain reasonable field mean profile water contents was unaffordable. In every case, the standard deviation increased in drier soil with obvious implications for use of soil water sensors in regulated deficit irrigation management. Many of the results of the multi-national IAEA study were published in a guide to field estimation of soil water content (Evett et al., 2008, Field Estimation of Soil Water Content: A Practical Guide to Methods, Instrumentation, and Sensor Technology. 131 pp. IAEA-TCS-30. International Atomic Energy Agency, Vienna, Austria. ISSN 1018-5518).
The capacitance sensors, though relatively poorly correlated with field measured soil water content, were very well self-correlated when measurements at the same depth and access tube were compared amongst sensors (Evett and Steiner, 1995, ibid; Evett et al., 2009, ibid). This indicated that capacitance sensors responded to some property of the soil-water system around the access tube that was not water content alone. Evett and Steiner (1995, ibid) hypothesized that this property was related to soil structure and non-uniform penetration into the soil of the EM field of the sensor. Studies of EM field penetration in heterogeneous materials showed over estimation of permittivity and uneven EM field penetration in those materials (e.g., Panteny et al., 2005 The frequency dependent permittivity and AC conductivity of random electrical networks. Ferroelectrics 319:199-208), supporting the inference that the EM field from a capacitance sensor is distorted by the individual arrangement of soil peds and pattern of water content in the peds around each access tube at each depth rather than being responsive to the mean water content of the soil around each access tube at each depth. This means that the geometric constant (fundamental to capacitance measurement theory) changes according to the small scale heterogeneity of soil properties at each measurement depth and access tube, which results in a different resonant frequency and water content estimate even if mean water content around the access tube is the same. Using a different EM sensor, Logsdon (2009, CS616 calibration: Field versus laboratory. Soil Sci. Soc. Am. J. 73:1-6) confirmed that uneven water contents in proximity to the sensor caused the sensor to overestimate water content. Several field studies have shown that capacitance and quasi-TDR sensors exhibit unrealistic spatial variability when compared with NP and volumetric gravimetric sampling (Evett et al., 2009, ibid; Heng et al., 2002, Comparison of soil moisture sensors between neutron probe, Diviner 2000 and TDR under tomato crops. Pp. 1532-1-1532-9 In Proc. 17th World Cong. Soil Sci., 14-21 August, Bangkok, Thailand).
Laboratory calibrations of capacitance sensors typically exhibit less accuracy than those from the NP or TDR. Calibrations were conducted in large soil columns (three replicates each of ground, sieved and repacked soil from the Ap, Bt, and calcic Bt horizons) by Evett et al. (2006, ibid). Calibration accuracy ranged from 0.018 to 0.058 m3 m−3 (RMSE of regression), comparable to values reported by Baumhardt et al. (2000, Soil material, temperature, and salinity effects on calibration of multisensor capacitance probes. Soil Sci. Soc. Amer. J. 64(6)1940-1946) and Paltineanu and Starr (1997, Real-time soil water dynamics using multisensor capacitance probes: Laboratory calibration. Soil Sci. Soc. Am. J. 61:1576-1585) for laboratory calibrations, but larger than the calibration accuracy of ≦0.01 m3 m−3 for conventional TDR and NP in the same study. Except for conventional TDR, laboratory calibrations did not, however, provide accurate soil water contents when used in the field (Evett et al., 2009, ibid). In the field, water contents were overestimated on the wet end and underestimated on the dry end; and values of change in profile water storage were relatively inaccurate for the capacitance sensors when compared with NP or gravimetric sampling. Subsequently, field calibrations of the NP and three capacitance sensor systems were conducted at the West Side Field Station in the San Joaquin Valley, Calif. (Mazahrih et al., 2008, ibid). Calibrations for the NP had high accuracy compared with those from the three capacitance sensors; and only three separate calibrations were needed to cover the 2-m deep profile over which the NP was calibrated. Also, the calibration for the depth range from 26 to 114 cm was only slightly different from that for the 131 to 201 cm depth range. In contrast, calibrations for the capacitance sensors were affected by increasing bulk electrical conductivity with depth, despite the fact that the sweet pepper crop in the drip irrigated field showed no salinity symptoms. Capacitance sensor calibration slopes increased strongly with depth; and the sensor frequency response to increasing water content became very small as depth increased, making the sensor output highly variable. Since the profile pattern of bulk electrical conductivity is expected to vary greatly across the field and with time (e.g., Burt et al., 2003, Long-term salinity buildup on Drip/Micro irrigated trees in California. In “Understanding & Addressing Conservation and Recycled Water Irrigation”, Proceedings of the International Irrigation Association Technical Conference. Pp. 46-56. November 2003; Hanson et al., 2003, Drip irrigation in salt affected soil. In “Understanding & Addressing Conservation and Recycled Water Irrigation”, Proceedings of the International Irrigation Association Technical Conference. Pp. 57-65. November 2003), these calibrations are essentially unusable for accurate soil water content estimation using the capacitance sensors.
Other examples of calibration errors increasing with soil bulk electrical conductivity were given by Baumhardt et al. (2000, ibid) and Evett and Schwartz (2009, Comments on “J. Vera et al., Soil water balance trial involving capacitance and neutron probe measurements”. Agric. Water Manage. 96:905-911). Geesing et al. (2004, Field calibration of a capacitance soil water probe in heterogeneous fields. Aust. J. Soil Res. 42:289-299) reported RMSE values of 0.03 to 0.04 m3 m−3 for field calibrations of the Diviner 2000 in loam and silt loam soils, respectively; and demonstrated the necessity of soil-specific calibration as have other authors (Baumhardt et al., 2000, ibid). For field calibrations at two sites, Polyakov et al. (2005, Calibration of a capacitance system for measuring water content of tropical soil. Vadose Zone J. 4:1004-1010) reported RMSE=0.031 and 0.048 m3 m−3 for calibration of a capacitance sensor system (EasyAg 50, Sentek, Pty., Ltd., Stepney, South Australia) in a kaolinitic silty clay loam in Hawaii. Although soil classification was the same, calibrations for the two sites (one was a hillslope and the other a nearby cultivated terrace) were clearly different. A laboratory calibration for the same soil using re-packed soil columns resulted in RMSE=0.039 m3 m−3. Results with capacitance sensors have tended to be better in sandy soils for which calibration coefficients tend to be similar (Robinson, 2001, Comments on “Field calibration of a capacitance water content probe in fine sand soils”. Soil Sci. Soc. Am. J. 65(5):1570-1571). However, sandy soils tend to have field capacity water contents <0.10 m3 m−3 (Morgan et al., 1999, Field calibration of a capacitance water content probe in fine sand soils. Soil Sci. Soc. Am. J. 63:987-989) and available water holding capacities of <0.04 m3 m−3, which places great demands on accuracy. Although Morgan et al. (1999, ibid) reported an RMSE of calibration of 0.0085 m3 m−3, other calibration studies have reported larger values for coarse textured soils. For example, data from a sandy to sandy loam soil in California resulted in RMSE=0.031 m3 m−3; and data from a loamy sand to sandy loam soil in Australia resulted in RMSE=0.016 m3 m−3 (Paltineanu and Starr, 1997, ibid). Both were laboratory calibrations using re-packed soil columns.
Existing capacitance systems are plagued by several problems. Oscillator frequency is dependent on water content; but, in the frequency range employed by these sensors, the permittivity is dependent on frequency; the result being a system with two unknowns but a single measurement. In the frequency range employed by capacitance sensors, the permittivity is also strongly influenced by the soil BEC and by the soil bound water content. Bound water is water so close to soil particle surfaces that the free rotation of the water molecule in an oscillating EM field is inhibited, changing the permittivity of the soil water system. The strength of the fringing field and the extent to which the EM field invades the soil outside the access tube is inversely proportional to the frequency, so attempts to avoid problems related to low frequencies are thwarted by the insensitivity of the measurement system that arises from using higher frequencies. The EM field invades a uniform medium with a well defined shape, but soil is highly structured and often does not act like a uniform medium at the EM frequencies used in capacitance sensors. In particular, the EM field preferentially invades more conductive soil volumes. Since the arrangement of soil structural elements around an access tube changes with location and depth in ways that are not predictable, a priori, the resonant frequency of the capacitance system is influenced by the closeness and arrangement of more conductive soil volumes. Soil BEC is a strong function of soil water content, meaning that soil water content variations at small scales near access tubes will impose small scale variations in soil BEC which will induce variations in EM field penetration into the soil and in frequency response of capacitance systems even if the larger scale soil volumetric water content is identical between two different realizations of the soil structure. Both soil BEC and bound water are strongly dependent on soil temperature, meaning that capacitance systems are temperature dependent, usually more so at larger soil water contents. Although at least one capacitance system now includes circuitry to measure soil BEC independently, no system exists that is free of temperature effects.
Both time domain reflectometry (TDR) and time domain transmission (TDT) systems attempt to measure the speed at which an electronic pulse transits an electrode that is in contact with the soil. Pulse speed decreases as soil water content increases. If the pulse travel time is a relatively simple function of the soil real electrical permittivity, ∈r, then the propagation velocity, vp, of the pulse is described byvp=co(∈rμ)−0.5  [3]where co is the speed of light in a vacuum, and μ is the magnetic permeability of the dielectric material (Topp et al., 1980, Electromagnetic determination of soil water content: Measurements in coaxial transmission lines, Water Resources Research, vol. 16, no. 3, pp. 574-582). However, for a TDR probe in a soil the dielectric material between the probe rods is a complex mixture of air, water and soil particles giving rise to dielectric losses such that the apparent permittivity, ∈a, has both real and imaginary parts:
                              ɛ          a                =                                            μɛ              ′                        2                    ⁢                      (                          1              +                                                {                                      1                    +                                                                  [                                                                              (                                                                                          ɛ                                relax                                ″                                                            +                                                                                                σ                                  dc                                                                                                  ω                                  ⁢                                                                                                                                          ⁢                                                                      ɛ                                    o                                                                                                                                                        )                                                    /                                                      ɛ                            ′                                                                          ]                                            2                                                        }                                0.5                                      )                                              [        4        ]            where ∈′ is the real component of the complex dielectric permittivity, ∈″relax is the imaginary component of permittivity due to relaxation losses, σdc/ω is the imaginary component of permittivity due to conductive (σdc) and frequency (ω) related dielectric losses and the other terms are previously defined. Although Eq. [4] is for a single frequency, it includes the effects that are important interferences to the EM methods. As the effective frequency decreases (e.g. due to low-pass filtering by coaxial cables, or due to the low base frequency of capacitance sensors and the declining frequency of these sensors with increasing soil water content), the value of σdc/ω increases, leading to larger values of ∈a. As conductivity increases (soils with larger BEC), the value of ∈a increases, more so at lower frequencies. And, as relaxation losses increase (e.g. bound water effects), the value of ∈a increases. For broad band signals such as that of TDR, the angular frequency (ω=2πf) may be replaced by an effective frequency, f (Robinson et al., 2003, A review of advances in dielectric and electrical conductivity measurement in soils using time domain reflectometry, Vadose Zone Journal, vol. 2, no. 4, p. 444), which previously has been calculated for TDR in at least four different ways (Schwartz et al., 2009a, Complex permittivity model for time domain reflectometry soil water content sensing. I. Theory. Soil Sci. Soc. Am. J. 73(3):886-897; Evett et al., 2005, TDR laboratory calibration in travel time, bulk electrical conductivity, and effective frequency. Vadose Zone J. 4:1020-1029; Or and Rasmussen, 1999, Effective frequency of TDR travel time-based measurement of bulk dielectric permittivity. Third Workshop on Electromagnetic Wave Interaction with Water and Moist Substances, Athens, Ga., USA, 11-13 Apr. 1999. Pp. 257-260; Topp et al., 2000, ibid).
The measured property in the TDR method is the travel time, tt, of the electronic pulse (voltage step) along the length (L) of the probe rods that are exposed to the soil (FIG. 1). The velocity of the pulse can be calculated as vp=2L/tr. Assuming μ=1, one sees that an apparent permittivity, ∈a, may be determined for a probe of known length, L, by measuring tt and rearranging Eq. [3], replacing ∈r with the more realistic ∈a, to obtain∈a=[cott/(2L)]2  [5]Topp et al. (1980, ibid) found that a single polynomial function described the relationship between volumetric water content, θv, and values of ∈a determined from Eq. [2] for four mineral soils.θv=(−530+292∈a−5.5∈a2+0.043∈a3)/104  [6]Since 1980, other researchers have shown that the relationship between θv and tt/(2L) is practically linear (e.g., Ledieu et al., 1986, A method of measuring soil moisture by time-domain reflectometry. J. of Hydrology 88, 319-328; Yu et al., 1997, Two- and three-parameter calibrations of time domain reflectometry for soil moisture measurement. Water Resour. Res. Vol. 33. No. 10, pp. 2417-2421). Indeed, Topp and Reynolds (1998, Time domain reflectometry: A seminal technique for measuring mass and energy in soil. Soil Tillage Res. 47(1,2): 125-132) found that the polynomial calibration of Topp et al. (1980, ibid) is usefully replaced by a linear equation in travel time: θv=0.115(cott/(2L))−0.176. We note here that the apparent permittivity, as calculated from travel time using Eq. [5], is affected by any deviation from unity of μ because μ was considered equal to unity in the derivation of Eq. [5]. In addition, the value of ∈a typically increases with the bulk electrical conductivity, σa (S m−1), of the soil, particularly for fine-textured super active soils (Wyseure et al., 1997, Measurement of volumetric water content by TDR in saline soils. Eur. J. Soil Sci. Vol. 48, pp. 347-354; Robinson et al., 2003, ibid), and particularly for σa>0.2 S m−1. Also, the value of σa increases with soil water content (Rhoades et al., 1976, Effects of liquid-phase electrical conductivity, water content, and surface conductivity on bulk soil electrical conductivity. Soil Sci. Soc. Am. J. Vol. 40. pp. 651-655; Mmolawa and Or, 2000, Root zone solute dynamics under drip irrigation: A review. Plant and Soil. Vol. 222. pp. 163-190). The value of ∈a may increase or decrease with temperature depending on the soil texture (Campbell, 1990, Dielectric properties and influence of conductivity in soils at one to fifty megahertz. Soil Sci. Soc. Am. J. Vol. 54, pp. 332-341; Pepin et al., 1995, Temperature-dependent measurement errors in time domain reflectometry determinations of soil water. Soil Sci. Soc. Am. J. Vol. 59, pp. 38-43; Persson and Berndtsson, 1998, Texture and electrical conductivity effects on temperature dependency in time domain reflectometry. Soil Sci. Soc. Am. J. Vol. 62, pp. 887-893; Wraith and Or, 1999, Temperature effects on soil bulk dielectric permittivity measured by time domain reflectometry: Experimental evidence and hypothesis development. Water Resour. Res. Vol. 35. No. 2, pp. 361-369), and increases as measurement frequency decreases (Campbell, 1990, ibid). The latter fact means that, for a broadband method such as TDR, there is a cable length effect because coaxial cable acts as a low pass filter—the longer the cable the less signal energy is present in the higher frequencies. The TDR estimated value of ∈a increases with cable length (Hook and Livingston, 1995, Reducing propagation velocity measurement errors in time domain reflectometry determinations of soil water, Soil Sci. Soc. Am. J, vol. 59, pp. 92-96), particularly for high surface area soils (Logsdon, 2000, Effect of cable length on time domain reflectometry calibration for high surface area soils. Soil Sci. Soc. Am. J. Vol 64, pp. 54-61). Topp et al. (2000, Impacts of the real and imaginary components of relative permittivity on time domain reflectometry measurements in soils. Soil Sci. Soc. Am. J. 64:1244-1252) found that TDR signal dielectric loss is a function of σa, regardless of whether this conductivity arises from soil water solution conductivity or from clay type and content. Thus, TDR calibrations should take σa into account, and probably cable length as well.
Although TDR is difficult to use deeply in soil profiles, the effects of bound water and σdc/ω for TDR are both smaller and better understood; and calibration methods exist that practically eliminate temperature and conductivity effects for TDR by taking into account the effective frequency and bulk electrical conductivity (Evett et al., 2005, ibid) and by taking into account these and the bound water content effect on ∈″relax (Schwartz et al., 2009a, ibid; Schwartz et al., 2009b, Complex permittivity model for time domain reflectometry soil water content sensing. II. Calibration. Soil Sci. Soc. Am. J. 73(3):898-909). And with TDR, the EM field generated by the voltage pulse is forced to pass along electrodes and be affected by both drier and wetter soil peds. That this results in a true average response to permittivity variations along the electrodes has been well established (Ferré et al., 1996, Spatial averaging of water content by time domain reflectometry: Implications for twin rod probes with and without dielectric coatings, Water Resources Research, 32(2):271-279; Hook and Livingston, 1995, ibid) which fact distinguishes TDR methods from the capacitance methods, which are influenced by the small-scale spatial arrangement of variations in soil water content and σa. If TDR methods can be made easier to apply, more reliable and amenable to deep measurement without soil disturbance, then TDR methods may eventually supplant the neutron probe for determinations of crop water use and water use efficiency.
Methods for accurate determination of TDR pulse travel time are not trivial as has been illustrated by Evett's (2000a, The TACQ Program for Automatic Time Domain Reflectometry Measurements: I. Design and Operating Characteristics. Trans. ASAE. 43(6):1939-1946; 2000b, The TACQ Program for Automatic Time Domain Reflectometry Measurements: II. Waveform Interpretation Methods. Trans. ASAE. 43(6):1947-1956) descriptions of waveform interpretation algorithms. Although similar to TDR in attempting to determine a pulse travel time, most of the TDT methods do not accurately determine travel time due to problems with their algorithms for pulse reflection analysis (Evett et al., 2006, ibid). Most TDT methods do not acquire a waveform and so cannot apply the graphical waveform analysis described by Evett (2000a, ibid; 2000b, ibid) and used in the TACQ program copyrighted by Evett in 1992. That prevents those methods from finding the true travel time. One exception is the TDT method described by Anderson (U.S. Pat. Nos. 6,657,443, 6,831,468) in which a waveform is acquired and graphical analysis is performed.
However, despite these and other advances, the need remains for improved techniques for determining soil water content and BEC.